Kolmogorov widths, Grassmann manifolds and unfoldings of time series

Buchstaber, V.M.

Автор: Buchstaber Victor Matveevich
Журнал: Sbornik Mathematics
Том: 216
Номер: 3
Год издания: 2025
Издательство: London Mathematical Society
Местоположение издательства: United Kingdom
Первая страница: 314
Последняя страница: 332
DOI: 10.4213/sm10240e
Аннотация: Problems in Kolmogorov's theory of widths and the theory of unfoldings of time series are considered. These theories are related by means of the theory of extremal problems on the Grassmann manifolds G(n,q) of q-dimensional linear subspaces of R^n. The necessary information on the manifolds G(n,q) is provided. Using an unfolding of a time series, the concept of the q-width of this series is introduced, and the q-width of a time series is calculated in the case of the functional of component analysis of the nodes of the unfolding. Using the Schubert basis of a q-dimensional linear subspace of R^n the concept of time series regression is introduced and its properties are described. An algorithm for the projection of a piecewise linear curve in R^n onto the space of unfoldings of time series is described and, on this basis, the concept of an L-approximation of a time series is introduced, where L is an arbitrary q-dimensional subspace of R^n. The results of calculations for discretizations of model functions and for time series obtained at a station monitoring the concentration of atmospheric CO_2 are presented.
Добавил в систему: Бухштабер Виктор Матвеевич

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Kolmogorov widths, Grassmann manifolds and unfoldings of time seriesстатья